Answer:
[tex]A = \dfrac{C^2}{4\pi}[/tex]
Step-by-step explanation:
Given that
Area of a circle [tex]A=\pi r^2[/tex]
Circumference of the circle [tex]C = 2 \pi r[/tex]
Let us re-write the equation of area of circle:
[tex]A=\pi r^2[/tex]
[tex]A = \pi \times r \times r[/tex]
Multiplying and dividing with 2:
[tex]A = \dfrac{2\pi r}{2} \times r\\\text{Putting }2\pi r = C:\\\Rightarrow A = \dfrac{C}{2} \times r\\\text{Multiplying and dividing by } 2\pi:\\\Rightarrow A = \dfrac{C}{2} \times \dfrac{2\pi r}{2\pi}\\\text{Putting }2\pi r = C:\\\Rightarrow A = \dfrac{C \times C}{4 \pi}\\\Rightarrow A = \dfrac{C^2}{4 \pi}[/tex]
Hence, A in terms of C can be represented as:
[tex]A = \dfrac{C^2}{4\pi}[/tex]
The answer Is not A
Answer:
B. 6, 8, 10 2/3, 14 2/9, 18 26/27
Step-by-step explanation:
The recursive relation tells you the first term is 6, eliminating choice A immediately.
It also tells you each term is 4/3 the previous term, so the sequence cannot be a sequence of integers*, eliminating choices C and D.
If you do the math, you find the terms of Choice B are correct:
6×4/3 = 88×4/3 = 10 2/3(10 2/3)×4/3 = 14 2/9..._____
* Unless you start with a very large power of 3, repeatedly multiplying by 4/3 will eventually end with powers of 3 in the denominator and some multiple of powers of 2 in the numerator. Such a ratio cannot be an integer.
Mrs. Williams wrote the following on the board during a math class.
Rule: Add 5
4,9, 14, ...
Which value belongs in this pattern?
A
27
B 45
С
D 142
need help please
Answer:
142
Step-by-step explanation:
Keep adding 5
What is 8478 to the nearest inch?
Answer: I’m guessing it would be 8478 because that doesn’t make sense
Step-by-step explanation:
Answer:
It is 8478
Step-by-step explanation:
What is the area of this figure?
Answer: 84
Step-by-step explanation: break down the parts and you multiply the sides and the answer to the square is 30 and the other half is 54 so 30 +54 =84
Which equation is equivalent to the following?
2x^2 – 12x + 2y^2 + 20y – 28 = 0
1) 2(x-3)^2+2(y+5)^2=44
2) 2(x-3)^2+2(y+5)^2=60
3) 2(x-3)^2+2(y+5)^2=62
4) 2(x-3)^2+2(y+5)^2=96
Answer:
4) 2(x - 3)^2 + 2(y + 5)^2 = 96.
Step-by-step explanation:
2x^2 – 12x + 2y^2 + 20y – 28 = 0
2(x^2 – 6) + 2(y^2 + 10y) = 28
2 ( (x - 3)^2 - 9)) + 2((y + 5)^2 - 25) = 28
2(x - 3)^2 - 18 + 2(y + 5)^2 - 50 = 28
2(x - 3)^2 + 2(y + 5)^2 = 28 + 18 + 50
2(x - 3)^2 + 2(y + 5)^2 = 96
Answer:
[tex]4) 2(x-3)^2+2(y+5)^2=96[/tex]
Step-by-step explanation:
[tex]2x^2 -12x +2y^2 + 20y - 28 = 0[/tex]
It basically represents a circle.
Equation of circle
[tex]\left(x-a\right)^2+\left(y-b\right)^2=r^2\:[/tex]
[tex]2x^2-12x+2y^2+20y=28[/tex]
[tex]$\frac{1}{2} (2x^2-12x+2y^2+20y)=28 \cdot \frac{1}{2} $[/tex]
[tex]x^2-6x+y^2+10y=14[/tex]
Organize the variables
[tex]\left(x^2-6x\right)+\left(y^2+10y\right)=14[/tex]
Now we have to complete the square for both groups:
[tex]\left(x^2-6x+9\right)+\left(y^2+10y+25\right)=14+9+25[/tex]
[tex]\left(x-3\right)^2+\left(y+5\right)^2=14+9+25[/tex]
[tex]\left(x-3\right)^2+\left(y+5\right)^2=48[/tex]
Now, I would proceed with:
[tex]\sqrt{48} =\sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3} =4\sqrt{3}[/tex]
[tex]\left(x-3\right)^2+\left(y+5\right)^2=(4\sqrt{3} )^2[/tex]
We got the center and the circle radius
[tex]\left(3,\:-5\right)\\r=4\sqrt{3}[/tex]
But this is not what you want:
So, just multiply both sides by 2 and you'll get:
[tex]2\left(x-3\right)^2+2\left(y+5\right)^2=96[/tex]
In what form is the following linear equation written?
v-3={(x - 1)
O A. Standard
O B. Point-slope
O C. Rise-run
O D. Slope-intercept
Answer:
B
Step-by-step explanation:
Point slope is in the form
(y - y1) = m(x - x1)
where x1 and y1 are the coordinate of any point on the line, and m is the slope
The others do not work
Answer:
B.
Step-by-step explanation:
This is the point-slope form:
y - y1 = m(x - 1) where m = the slope.
Looks like you have a typo in your equation.
HELP QUICK
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 280 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden. The length of the garden is ? feet.
Answer:
84ft
Step-by-step explanation:
w = 2/3(L)
if 280 feet of fencing can enclose the garden,therefore the perimeter is 280 feet
perimeter = 2L + 2W
but W=2/3(L)
therefore, perimeter = 2L + 2(2/3L)
P= 2L + 4/3(L)
P= 10/3(L)
but P= 280
therefore 280= 10/3(L)
L = (3×280)÷10
L= 84 feet
Consumer Math work. Please help
Mr. Cruz earns $11.25 an hour at his part-time job. Last week he worked 30 hours. What was his gross pay for the week? Another way of asking this question is; how much is she paid before taxes and deductions are subtracted? *
Answer:
$337.5
Step-by-step explanation:
He would get $337.5 because if he gets $11.25 every hour you just multiply $11.25 by 30 hours.
Can someone please help me?
Let θ be an angle in quadrant IV such that sinθ=-3/4. Find the exact values of secθ and cotθ.
cos2(θ) + sin2(θ) = 1
sec(θ) = 1/cos(θ)
cot(θ) = cos(x)/sin(θ)
sin(θ) = -3/4
cos2(θ) + sin2(θ) = 1
cos2(θ) = 1 - sin2(θ)
cos2(θ) = 1 - 9/16 = 7/16
cos(θ) = ±√(7/16) = √7/16 (cosine is positive in Q IV)
sec(θ) = 1/cos(θ) = 4/√7
cot(θ) = cos(θ)/sin(θ) = (4/√7)/(-3/4) = -16√7/21
The exact values of secθ = 4/√7 and cotθ = -16√7/21
What is Trigonometric functions?Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.
Given that,
sinθ = -3/4
∵sin²(θ) +cos²(θ) = 1
∴cos²(θ) = 1 - sin²(θ)
cos(θ) = √(1 - sin²(θ))
cos²(θ) = √(1 - 9/16 )
cos(θ) = ±√(7/16) = √7/4 (cosine is positive in quadrant IV )
sec(θ) = 1/cos(θ) = 4/√7
∵cot(θ) = cos(θ)/sin(θ)
∴cot(θ)= (4/√7)/(-3/4)
cot(θ) = -16√7/21
The exact values of secθ = 4/√7 and cotθ = -16√7/21
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Help me please I don’t understand
Answer:
14/11
Step-by-step explanation:
A rational number times a rational number is rational
A rational number is written as a/b
14/11 * 1/2 = 7/11
This is rational
The expression x^2 + x + b is a perfect square trinomial. What is the value of b?
Answer:
1/4
Step-by-step explanation:
x^2+x+b= x^2+2*x+1/2+(1/2)^2= (x+1/2)^2
b= 1/4
Level 1
R.18 Identify equivalent linear expressions II KAR
Select the expressions that are equivalent to -7(75 + 1).
75-7
7(-75 + 1)
-7(-5 + 8 + 1)
-7s - 49
Write the slope intercept form Through:(1,-5) and(4, -1)
Answer:
Slope intercept form is
[tex]y=\frac{4}{3} x- \frac{19}{3}[/tex]
A beverage manufacturer performs a taste-test and discovers that people like
their fizzy beverages best when the radius of the bubbles is about 0.7 mm.
According to the formula below, what would be the volume of one of these
bubbles?
Answer:
The Answer is: B= about 1.44mm^3
Step-by-step explanation:
hope I could help you out :)
The volume of bubble is 1.44 cubic mm.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation : Divides left hand operand by right hand operand
Given data as :
Radius of the Bubble (r) = 0.7 mm
Volume of the bubble is given by the formula
[tex]r =\sqrt[3]{\dfrac{3v}{4\pi} }[/tex]
Taking cube on both sides
r³ = 3v/4π
Rearrange the equation,
v = 4πr³/3
Substitute the value of r in the above equation,
v = 4π(0.7)³/3
Substitute the value of π = 3.14
v = 4(3.14)(0.343)/3
v = 4.3/3
v = 1.44
Hence, the volume of bubble is 1.44 cubic mm.
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What is an equation of circle O shown in the graph below?
(1) x2 + 10x + y2 + 4y = -13
(2) x2 - 10x + y - 4y = -13
(3) x + 10x + y + 4y = - 25
(4) r2 - 10x + y- 4y = - 25
Answer:
Equation of circle is [tex]x^2+y^2-12x-4y+24=0[/tex]
None of the options is correct
Step-by-step explanation:
Given: Graph
To find: equation of circle
Solution:
A circle is a locus of all points that are at a fixed distance (radius) from a fixed point (centre).
From the graph,
centre (a, b) = [tex]\left ( 6,2 \right )[/tex]
radius (r) = 4 units
Equation of circle is of form [tex](x-a)^2+(y-b)^2=r^2[/tex]
[tex](x-6)^2+(y-2)^2=4^2\\x^2+36-12x+y^2+4-4y=16\\x^2+y^2-12x-4y+24=0[/tex]
The equation of circle is [tex]x^2+y^2-12x-4y+24=0[/tex]
None of the options is correct
We have given the graph
We have to determine the equation of circle
A circle is a locus of all points that are at a fixed distance (radius) from a fixed point (centre).
From the graph,
centre (a, b) = (6,2)
radius (r) = 4 units
What is the equation of a circle?Equation of circle is of form
[tex](x-a)^2+(y-b)^2=r^2[/tex]
[tex](x-6)^2+(y-2)^2=4^2\\x^2-12x+36+y^2-4y+4=16\\x^2+y^2-12x-4y+24=0[/tex]
Therefore the equation of the circle is [tex]x^2+y^2-12x-4y+24=0[/tex]
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The dimensions of triangle A are twice the dimensions of triangle B. The area of triangle A is 162 cm2.
What is the area of triangle B?
Answer:
40.5 cm²
Step-by-step explanation:
Given the ratio of sides of 2 figures = a : b
then the ratio of areas = a² : b²
Here the ratio of Δ A : Δ B = 2 : 1, thus
ratio of areas = 2² : 1² = 4 : 1
That is the area of Δ A is 4 times area of Δ B, so
area of Δ B = 162 ÷ 4 = 40.5 cm²
Answer:
81
Step-by-step explanation:
162/2=81
Ms. Sculley needs to arrange 28 chairs into equal rows. She needs more than 2 chairs in each row and more than 2 rows. How many rows will she have?
Answer: 7 rows
Step-by-step explanation:
she will have 7 rows with 4 seats in each row or 4 rows with 7 seats in each row
A four-person committee is chosen from a group of eight boys and six girls. If students are chosen at random, what is the probability that the committee consists of all boys? StartFraction 4 Over 1001 EndFraction StartFraction 15 Over 1001 EndFraction
Answer:
10/143
Step-by-step explanation:
got 100%
When students are chosen at random, the probability that the committee consists of all boys is 10/143.
What is probability?Probability simply means the likelihood that a particular thing will occur. It's due to chance or luck.
In this case, when students are chosen at random, the probability that the committee consists of all boys is 10/143.
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3 over 2 divided by 8 over 3
Answer:
Step-by-step explanation:
3/2/8/3
=9/16
Answer:
9/16
Step-by-step explanation:
3/2 ÷ 8/3
Here, we are trying to divide fractions.
When dividing fractions, you can flip the second fraction, and multiply the fractions together.
Hence, our new expression would be:
3/2*3/8
We can multiply the numerators together and the denominators together.
3*3/2*8
9/16
Help, What is the answer?
Answer:
probably jay z albulm 4:44
Step-by-step explanation:
Place the indicated product in the proper location on the grid. (b2 + 8 )(b2 - 8)
Step-by-step explanation:
(b2 + 8 )(b2 - 8)(b2 + 8 )(b2 - 8)=b4 - 8b2 + 8b2 - 64(b2 + 8 )(b2 - 8)=b4 - 8b2 + 8b2 - 64=b4 - 647. Piper Rothermel's credit card has a $926.42 balance. She makes a $223.50 payment. What is the new balance?
A $1,149.92
B $702.92
C$685.90
D$782.43
I NEED THIS ANSWER RN PLS
Answer:
The answer is 702.92 or answer B
Step-by-step explanation:
Use subtraction.
928.42 - 223.50 = 702.92
Hello ! ^^
• What's the new balance ?
→ b. $702.92
bc : 926.42 - 223.50 = 702.92
✘ i hope i helped you ! ✘
five less than 2 times a number is equal to the sum of the number and 3. What is the number?
Answer:
Value of Number = 8
Step-by-step explanation:
Consider the equation below;
[tex]If x - " A Number " -\\( 2 * x ) - 5 = x + 3,\\[/tex]
Now using this equation let us solve for x;
[tex]( 2 * x ) - 5 = x + 3 - Take ( 2 * x ) - 2x,\\2x - 5 = x + 3 - Add 5 on Either Side,\\2x = x + 8 - Subtract x From Either Side,\\\\x = 8, ( Solution )\\\\Conclusion ; x = 8[/tex]
Knowing this, we can say;
[tex]Value of Number = 8,\\if x - Value of Number ( Given ),\\\\Solution ; Value of Number = 8[/tex]
The value of unknown number x will be 8.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have been given a statement as;
"five less than 2 times a number is equal to the sum of the number and 3"
Let the unknown number be x.
So, from the given statement,
2x- 5 = x + 3
Subtract x on both sides;
2x- 5 = x + 3
2x- 5 -x = x + 3 - x
x - 5 = 3
Add 5 on both sides;
x - 5 = 3
x = 8
Therefore, the value of unknown number x will be 8.
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A rectangular piece of cardboard that is 7 inches by 20 inches has squares of length x inches on a side cut from each corner.
(Assume that 0 < x < 3.) Represent the remaining area in the form of a polynomial function A(x).
Answer:
The remaining area in the form of a polynomial function [tex]A(x)= 140-4x^2[/tex]where 0 < x < 3.
Step-by-step explanation:
Breadth of rectangular piece of cardboard = 7 inches
Length of rectangular piece of cardboard = 20 inches
Area of cardboard = [tex]Length \times Breadth[/tex]
Area of cardboard = [tex]20 \times 7[/tex]
Area of cardboard =[tex]140 in^2[/tex]
Squares of length x inches on a side cut from each corner.
Length of square = x
Area of 1 square = [tex]Side^2 = x^2[/tex]
Area of 4 squares = [tex]4x^2[/tex]
Area of remaining portion [tex]A(x)= 140-4x^2[/tex]
So, the remaining area in the form of a polynomial function [tex]A(x)= 140-4x^2[/tex]where 0 < x < 3.
Identify the coordinates of the vertex of f(x) = (x – 3)2 + 14, and identify whether it's an absolute minimum or absolute maximum.
Which is correct:
A) (–3, 14), absolute maximum
B) (3, 14), absolute minimum
C) (3, 14), absolute maximum
D) (–3, 14), absolute minimum
Answer:
The answer is option B.
Hope this helps.
Answer:
B
Step-by-step explanation:
Which graph shows the solution to the inequality -3x-7 <20?
Answer:
x > -9
Step-by-step explanation:
The solution to the inequality is obtained as follows:
-3x -7 < 20
-3x - 7 + 7 < 20 + 7
-3x < 27
-3x/(-3) > 27/(-3)
x > -9
Notice that when you divide by a negative number, the inequality sign changes.
In the picture attached, the graph of the solution s shown. Notice that -9 is not included in the solution.
1
0
1
Which equation matches the number line?
S
2+ (4)
1
1
3
1
1
Answer:
The ans from the bottom left
Find the value of d, the length of the diagonal across the square. If necessary,
round your answer to 2 decimal places.
Answer:
Step-by-step explanation:
Use Pythagorean theorem,
d² = 4² + 4²
= 16 + 16
d² = 32
d = √32
d = 5.67 units
Which ordered pair is generated from the equation shown below?
y = 3x + 2
O A) (3, 11)
OB) (3,9)
OC) (5, 15)
OD (2,4)
Answer:
A
Step-by-step explanation:
let's try A. 3(3)+2=9+2=11
11=11
So A is right